ม1 พื้นฐาน เทอม 1 เล่ม 1

ï190 ÒáĂãöĀøãñìŝ çąē ÞĀç Ċåûï 5. 48300  (2.4  104 = (4.83  104  (2.4  104 = (4.83  2.4  (104  104 = 11.592  108 = 1.1592  10  108 = 1.1592  109 . “ĵΔ´Ç «šÄÛ «¹«©³ÇÖ –Ç Äf «g¿´ Ô Ñ½g¿´ËfÑ«µË­¼ÃŸ“µ¥¹©Æ ´ÄºÄ¼§µ Μf« 0.03 = 1030 = 1032 = 3  102 0.045 = 104050 = 4.51000 10 = 41.050 = 4.5  102 1070000 = 1705 = 7  105 0.00007 = 1007,.0300 = 7.3 0.000073 = 105 = 7.3  105 0.0000738 = 1070.3,0800 = 71.0358 = 7.38  105 §Ã¹¿´Äf ™©ÖÇ  š™Î”Ç´«šÛÄ«¹«§f¿Ò­«Ç× Ñ½¿g ´ËfÑ«µ­Ë ¼ŸÃ “µ¥¹ ©Æ ´ÄºÄ¼§µ 1. 0.0004 = 10,0400 = 1404 = 4  104 2. 0.00045 = 104,0.500 = 140.54 = 4.5  104 3. 0.000453 = 140.,50300 = 41.0543 = 4.53  104 4. 0.00453 = 14,.05030 = 41.0533 = 4.53  103 41.0503 = 4.53 5. 0.0453 = 102 = 4.53  102 6. 0.453 = 41.503 = 4.53  101 7. 0.0008 = ........................................................................................................ 8. 0.0057 = ........................................................................................................ 9. 0.0875 = ........................................................................................................

ĊóÐðÏÏĀė óÕÿ 191 10. 0.0000007938 = ............................................................................................ 11. 0.4000385 = ............................................................................................ 12. 0.00000000000012 = ............................................................................................ §Ã¹¿´Äf ™©ÇÖ š™Î”Ç´«šÄÛ «¹« ©ÖÇÏ©«¼ÃŸ“µ¥¹ ©Æ ´ÄºÄ¼§µÑ «Ï§·f ”g¿§f¿Ò­«×Ç 1. 8  104 = 0.0008 2. 1.2  105 = 0.000012 3. 5  103 = 0.005 4. 3.78  106 = 0.00000378 5. 7.123  108 = ................................................................................................ 6. 1.32  104 = ................................................................................................ 7. 6.35  102 = ................................................................................................ 8. 4.325  103 = ................................................................................................ 9. 1.7389  104 = ................................................................................................ 10. 5.1463  103 = ................................................................................................

ï192 ÒáĂãöĀøãñŝìąēçÞĀç Ċåûï E\"\"%Ă 39 L= e 1. š™Î”´Ç «šÄÛ «¹«§f¿Ò­«×Ç Ñ½¿g ´ÑfË «µ­Ë @  1M γ¿ÉÖ 1 d < 1 Ï·Â M D#đ!šÄÛ «¹«Î§Õ³ 1. 80 = ......................................................................................... 2. 200 = ......................................................................................... 3. 500 = ......................................................................................... 4. 4,000 = ......................................................................................... 5. 70,000 = ......................................................................................... 6. 300,000 = ......................................................................................... 7. 4,000,000 = ......................................................................................... 8. 80,000,000 = ......................................................................................... 9. 900,000,000 = ......................................................................................... 10. 60,000,000,000 = ......................................................................................... 11. 78 = ......................................................................................... 12. 240 = ......................................................................................... 13. 560 = ......................................................................................... 14. 4,800 = ......................................................................................... 15. 78,500 = ......................................................................................... 16. 350,000 = ......................................................................................... 17. 459,700 = ......................................................................................... 18. 89,400,000 = ......................................................................................... 19. 930,100,000 = ......................................................................................... 20. 63,501,000,000 = ......................................................................................... 22. 900,000 = ......................................................................................... 23. 360,000 = ......................................................................................... 24. 570,000,000 = .........................................................................................

ĊóÐðÏÏĀė óÕÿ 193 25. 1,32,400,000,000 = ......................................................................................... 26. 5,471,000,000 = ......................................................................................... 27. 202,000,000 = ......................................................................................... 28. 4,200,000,000 = ......................................................................................... 29. 1,012,000,000 = ......................................................................................... 30. 532,000,000,000,000 = ......................................................................................... . š™Î”´Ç «šÛÄ«¹«§f¿Ò­«Ç× Ñ½¿g ´ÑfË «µ­Ë @  1M γ¿ÖÉ 1 d < 1 Ï·Â M D#đ!šÄÛ «¹«Î§Õ³ 1. 0.8 = ......................................................................................... 2. 0.004 = ......................................................................................... 3. 0.00005 = ......................................................................................... 4. 0.000007 = ......................................................................................... 5. 0.0000009 = ......................................................................................... 6. 0.00000003 = ......................................................................................... 7. 0.084 = ......................................................................................... 8. 0.00457 = ......................................................................................... 9. 0.0000573 = ......................................................................................... 10. 0.000000712 = ......................................................................................... 12. 0.00035 = ......................................................................................... 13. 0.00027 = ......................................................................................... 14. 0.000314 = ......................................................................................... 15. 0.02101 = ......................................................................................... 16. 0.000364 = ......................................................................................... 17. 0.0000199 = ......................................................................................... 18. 0.000083 = ......................................................................................... 19. 0.0000003 = ......................................................................................... 20. 0.0000212 = .........................................................................................

ï194 ÒáĂãöĀøãñìŝ ēąçÞĀç Ċåûï 21. 0.0001836 = ......................................................................................... 22. 0.00002189 = ......................................................................................... 23. 0.000002346 = ......................................................................................... 24. 0.00000029 = ......................................................................................... 25. 0.00001331 = ......................................................................................... 26. 0.00001241 = ......................................................................................... 27. 0.0000015 = ......................................................................................... 28. 0.00000201 = ......................................................................................... 29. 0.00010102 = ......................................................................................... 30. 0.000002103 = ......................................................................................... . š™Î”´Ç «šÛÄ«¹«§f¿Ò­«Ç× Ñ«µË­  1M γÖÉ¿ 1 d < 1 Ï·Â M D#đ!šÄÛ «¹«Î§³Õ 1. 45  103 = (4.5  10  103 = 4.5  104 2. 0.45  103 = (4.5  101  103 = 4.5  104 3. 780  104 = ............................................................................................ = ............................................................................................ 4. 0.78  104 = ............................................................................................ = ............................................................................................ 5. 2300  108 = ............................................................................................ = ............................................................................................ 6. 0.00075  106 = ............................................................................................ = ............................................................................................ 7. 450  105 = ............................................................................................ = ............................................................................................

ĊóÐðÏÏĀė óÕÿ 195 8. 0.0045  108 = ............................................................................................ = ............................................................................................ 9. 12,300  108 = ............................................................................................ = ............................................................................................ 10. 0.000075  104 = ............................................................................................ = ............................................................................................ 11. 0.000123  102 = ............................................................................................ = ............................................................................................ 12. 108,000  105 = ............................................................................................ = ............................................................................................ 13. 0.000095  103 = ............................................................................................ = ............................................................................................ 14. 18,000,000  103 = ............................................................................................ = ............................................................................................ 15. 23,000,000  108 = ............................................................................................ 16. 28  105 = ............................................................................................ 17. 109  104 = ............................................................................................ 18. 0.0066  108 = ............................................................................................ 19. 0.00093  104 = ............................................................................................ 20. 47  108 = ............................................................................................ 21. 965  106 = ............................................................................................ 22. 340  109 = ............................................................................................ 23. 0.102  108 = ............................................................................................ 24. 0.0025  108 = ............................................................................................ 25. 623  1010 = ............................................................................................ 26. 0.0001  107 = ............................................................................................

ï196 ÒáĂãöĀøãñŝìçąē ÞĀç Ċåûï 27. 684.2  106 = ............................................................................................ 28. 156.2  103 = ............................................................................................ 29. 0.0217  105 = ............................................................................................ 30. 21,700  107 = ............................................................................................ . ¼ŸÃ “µ¥¹©Æ ´ÄºÄ¼§µ ϧ·f ”¿g §¿f Ò­«Ç×Ï©«šÄÛ «¹«Ñ¦ 1. 5  104 = ............................................................................................ 2. 7  106 = ............................................................................................ 3. 8  103 = ............................................................................................ 4. 6  105 = ............................................................................................ 5. 1.5  106 = ............................................................................................ 6. 7.23  108 = ............................................................................................ 7. 4.5  103 = ............................................................................................ 8. 9.14  105 = ............................................................................................ 9. 2.789  107 = ............................................................................................ 10. 1.0084  108 = ............................................................................................ 11. 3.12  105 = ............................................................................................ 12. 5.4  105 = ............................................................................................ 13. 212  106 = ............................................................................................ 14. 518  109 = ............................................................................................ 15. 7.54  106 = ............................................................................................ 16. 8.42  109 = ............................................................................................ 17. 4.93  108 = ............................................................................................ 18. 9.021  106 = ............................................................................................ 19. 8.24  103 = ............................................................................................ 20. 3.72  105 = ............................................................................................

ĊóÐðÏÏĀė óÕÿ 197 21. 5.16  108 = ............................................................................................ 22. 4.61  107 = ............................................................................................ 23. 6.25  1011 = ............................................................................................ 24. 4.3  106 = ............................................................................................ 25. 4.96  109 = ............................................................................................ 26. 7.8  108 = ............................................................................................ 27. 9.024  1010 = ............................................................................................ 28. 1.08  109 = ............................................................................................ 29. 2.108  1011 = ............................................................................................ 30. 1.6008  1010 = ............................................................................................ . ¨gļ³¿™–«³«Ç ÛÄ× ½«Ã“Λ·Ç´Ö 1.  1- ΩfĔ¿™«Û׼«“à §Ã¹ ³Ä«Ç½«Ã“  “ÐÆ ·“µÃ³ šÂ³«Ç ÛÄ× ½«“à ”¿™¼³¿™­µÂ³Ä¥Î©Äf Ѧ .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. . ½¹Ã њ”¿™³«Ê»´Χ«g ­µÂ³Ä¥  –µ™×à §f¿«Ä©Ç š™½Ä¹fÄѫι·Ä 1 ¹Ã« ½¹Ã њšÂΧg«“Öǖµ×™Ã .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. ..............................................................................................................................................

ï198 ÒáãĂ öĀøãñŝìçąē ÞĀç Ċåûï 7. ©Ä™œÄg ™Î®¿É “³ÎÇ ¼«g ®Äf º«Ë ´“ ·Ä™´Ä¹­µÂ³Ä¥ 1 ­Ï^ ¼™ š™½Ä¹Äf ©Ä™œÄg ™Î®¿É “³ÎÇ ¼«g ®Äf º«Ë ´“ ·Ä™ ´Ä¹Î©fÄѦ 1 ­^ϼ™´Ä¹­µÂ³Ä¥ .  11 “ÐÆ ·Î³§µ .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. . з“½³«Ê µ¿¬¦¹™¿Ä©§Æ ´ Ñ«¿§Ã µÄεչ­µÂ³Ä¥ .  17 “Æз㧵§¿f ¹«Æ Ä©Ç Ñ«Î¹·Ä 1 œ³. šÂ³¿Ç §Ã µÄε¹Õ ΩfÄѦ .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. . ¦Ä¹Î–µÄ½«¿g ´ ³µÇ ­Ë µfę–·gÄ´½¹Ã ³«Ã ¯µÃ™Ö Жšµ¿´ËÑf «¿¹“ĺ ¿´Ëf½fęšÄ“з“­µÂ³Ä¥ .  1 “Æз㧵 ¦Ä¹Î–µÄ½«¿g ´ ½fęšÄ“з““Ö“Ç ÐÆ ·Î³§µ .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. ..............................................................................................................................................

ĊóÐðÏÏĀė óÕÿ 199 1. Ò¹µÃ¼³Ç–¹Ä³´Ä¹Î›·ÇÖ´­µÂ³Ä¥ .1  1- Ν«§Æ㧵 Îά–©ÇεǴ”«Ä¦Ñ½Ÿf´Ä¹­µÂ³Ä¥   1- Ν«§ÎÆ ³§µ š™½Ä¹Äf Ò¹µÃ¼´Ä¹D#đ!“ÖÎÇ ©Äf ”¿™Ï¬–©ÇεǴѽŸf .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. ..............................................................................................................................................

ï200 ÒáĂãöĀøãñŝìąçē ÞĀç Ċåûï E\"\"25\" š™Î·É¿“–ÄÛ §¿¬©Ç¨Ö “Ë §g¿™©¼ÇÖ ¦Ê η”´““ÛķÙ 1. 43 ¿Äf «¹Äf ¿´Äf ™Òµ “. ¼Öǖ˥¼Ä³ ”. ¢Ä«¼ÇœÖ ×ǓÄÛ ·Ã™¼Ä³ –. ¼ÇÖ´““Ûķټij ™. ¼Ä³¢Ä«“ÄÛ ·Ã™¼ÖÇ 2. (52 ¿Äf «¹fÄ¿´Äf ™Òµ ”. ¢Ä«·¬½gÄ œ“Ç× ÛķÙ¼¿™ “. ·¬½Äg –¥Ë ¼¿™ ™. ¼¿™¢Ä« “ÄÛ ·Ã™·¬½Äg –. ·¬½Äg ´““ÄÛ ·Ã™¼¿™ 3. 32 ³šÇ ÄÛ «¹«Ñ¦D#đ!¢Ä« Ï·Âη”œÇדÛķÙ “. ¢Ä«D#đ! 3 η”œÇדÛķÙD#đ! 2 ”. ¢Ä«D#đ! 3 η”œÇ“× ÛÄ·™Ã D#đ! 2 –. ¢Ä«D#đ! 3 η”œÇ“× ÛķÙD#đ! 2 ™. ¢Ä«D#đ! 3 η”œ“Ç× ÛķÙD#đ! 2 4. (24 ³šÇ ÛÄ«¹«Ñ¦D#đ!¢Ä« Ï·Âη”œÇדÛķÙ “. ¢Ä«D#đ! 2 η”œ“×Ç ÛÄ·™Ã D#đ! 4 ”. ¢Ä«D#đ! 2 η”œÇדÛķÙD#đ! 4 –. ¢Ä«D#đ! 2 η”œ×“Ç ÛķÙD#đ! 4 ™. ¢Ä«D#đ! 2 η”œÇדÄÛ ·™Ã D#đ! 4 5. 24 Ï©«šÛÄ«¹«Ñ«”g¿Ñ¦§f¿Ò­«Ç× ”. 8 “. 4 ™. 32 –. 16

ĊóÐðÏÏĀė óÕÿ 201 6. 24 Ï©«šÄÛ «¹«Ñ«”g¿Ñ¦§¿f Ò­«Ç× ”. 16 “. 4 ™. 16 –. 4 7. 50 Ï©«šÄÛ «¹«Ñ«”¿g Ѧ§f¿Ò­«Ç× ”. 5 “. 1 ™. 50 –. 15 8. (80 Ï©«šÛÄ«¹«Ñ«”¿g Ѧ§¿f Ò­«×Ç ”. 1 “. 1 ™. 8 –. 8 9. (0.23 Ï©«šÄÛ «¹«Ñ«”¿g Ѧ§¿f Ò­«×Ç ”. 0.16 “. 0.8 ™. 0.016 –. 0.008 10. (0.24 Ï©«šÛÄ«¹«Ñ«”¿g Ѧ§f¿Ò­«×Ç ”. 0.016 “. 0.8 ™. 0.000016 –. 0.0016 11. (x + 2X3 ³–Ç Äf ΩÄf Ѧ Î³Ö¿É “ÛĽ«¦ x = 2 Ï·Â X = 3 “. 125 ”. 216 –. 843 ™. 512 12. ¨Äg 2x = 64 š™½Ä–fÄ x ”. 5 “. 4 ™. 7 –. 6

ï202 ÒáĂãöĀøãñìŝ ēąçÞĀç Ċåûï 13. ¨gÄ 73 = 49 š™½Ä–Äf  ”. 4 “. 5 ™. 2 –. 3 14. 34  37 Ò¦®g ··°Ã ª§µ™“¬Ã ”g¿Ñ¦§f¿Ò­«×Ç “. 311 ”. 33 –. 611 ™. 63 15. 8  23  32 Ò¦g®··Ã°ª§µ™“¬Ã ”¿g Ѧ§¿f Ò­«Ç× “. 210 ”. 40  23 –. 23 ™. 211 16. (4m2n  (5mn4 Ò¦g®··°Ã ª§ µ™“씿g Ѧ§f¿Ò­«×Ç “. 1m3n5 ”. 20m3n5 –. m3n5 ™. 20m3n5 17. 3m  3n  38 Ò¦®g ··Ã°ª§ µ™“ì”g¿Ñ¦§f¿Ò­«×Ç “. 38mn ”. 3m+n+8 –. 98mn ™. 9m+n+8 18. 50 + 21 ³Ç–Äf ΩÄf “ì”g¿Ñ¦§¿f Ò­«×Ç ”. 3 “. 2 ™. 9 –. 7 19. 34 ³–Ç Äf Ωfē¬Ã ”g¿Ñ¦§¿f Ò­«Ç× ”. 12 “. 12 ™. 34 –. 134

ĊóÐðÏÏĀė óÕÿ 203 20. 215 ³–Ç Äf Ωfē¬Ã ”¿g Ѧ§f¿Ò­«×Ç ”. 32 ™. 25 “. 32 –. 25 21. 23 32 34 ©ÄÛ Ñ½Dg #đ!µË­¿´Äf ™™Äf ´ Ï·Âη”œÇדÛÄ·™Ã D#đ! §µ™“씿g Ѧ “. 23  32 ”. 23  32 –. 2323 ™. 3223 22. 8@2@3A54BB3 ³Ç–Äf §µ™“씿g Ѧ§¿f Ò­«Ç× ”. 4@2A4B4 “. 4@2 ™. 4@B22A4 A4B2 –. 4B@22A4 23. mm25nn3 3 ³Ç–fħµ™“ì”g¿Ñ¦§¿f Ò­«×Ç ”. m21n6 “. m9n12 ™. m21n12 –. m9n6 24. –Äf ”¿™ 43  32 §µ™“¬Ã ”g¿Ñ¦§f¿Ò­«Ç× ”. 10 ™. 3 “. 55 –. 6 25. –Äf ”¿™ 53 + 33 §µ™“¬Ã ”g¿Ñ¦§¿f Ò­«Ç× ”. 52 ™. 512 “. 24 –. 152

ï204 ÒáãĂ öĀøãñìŝ ēąçÞĀç Ċåûï 26. –fĔ¿™ (42  223 §µ™“¬Ã ”g¿Ñ¦§f¿Ò­«Ç× “. 36 ”. 64 –. 512 ™. 1728 27. –Äf ”¿™ 32 + 25 §µ™“씿g Ѧ§¿f Ò­«Ç× “. 41 ”. 23 –. 41 ™. 23 28. –Äf ”¿™ (322  (232 §µ™“¬Ã ”¿g Ѧ§¿f Ò­«Ç× “. 145 ”. 145 –. 17 ™. 17 29. –fĔ¿™ 32  22 §µ™“씿g Ѧ§f¿Ò­«Ç× (32 + 221 “. 1 ”. 1 –. 132 ™. (132 30. –Äf ”¿™ 32 + 33 + 34 + 35 §µ™“¬Ã ”g¿Ñ¦§f¿Ò­«×Ç “. 314 ”. 1214 –. 360 ™. 480

ìçēą ÞĀçåĀÕĊñÐĀÒáãĂ 205 31. –fĔ¿™ 32  273  81 ΩÄf “¬Ã ”g¿Ñ¦§¿f Ò­«×Ç “. 315 ”. 316 –. (277 ™. (274 32. –fĔ¿™ (62  (154  (356 ΩÄf “¬Ã ”¿g Ѧ§f¿Ò­«×Ç (1056 “. 52 ”. 22  54 –. 152 ™. 54 23 73 33. (9  106 + (7  105  (52  105 ³–Ç fħµ™“ì”g¿Ñ¦§¿f Ò­«Ç× “. 7.2  103 ”. 7.2  104 –. 7.2  105 ™. 7.2  106 34. ”¿g ѦΔ´Ç « 8,750,000 Ñ«µË­”¿™¼ÃŸ“µ¥¹©Æ ´ÄºÄ¼§µÒ¦g¨Ë“§g¿™ “. 2.5  106 ”. 2.5  105 –. 2.5  104 ™. 2.5  103 35. ”¿g ѦΔǴ« 8,750,000 Ñ«µË­”¿™¼ŸÃ “µ¥¹©Æ ´ÄºÄ¼§µÒ ³f¨“Ë §g¿™ “. 875  106 ”. 8.75  106 –. 875  104 ™. 8.75  104

ï206 ÒáãĂ öĀøãñìŝ çēą ÞĀç Ċåûï 36. ”g¿Ñ¦Î”Ç´« 0.000475 Ñ«µ­Ë ”¿™¼ÃŸ“µ¥¹ ©Æ ´ÄºÄ¼§µÒ¦¨g ˓§g¿™ “. 475  103 ”. 4.75  103 –. 475  104 ™. 4.75  104 37. 23.645  104 Δ´Ç «¿´fËÑ«µË­ A  10n, 1 d A  10 Ï·Â n D#đ!šÄÛ «¹«Î§Õ³ Ò¦g ¦™Ã ”g¿Ñ¦ §¿f Ò­«×Ç “. 2.3645  104 ”. 2.3645  105 –. 23645  104 ™. 23645  105 38. 36.658  108 ΔǴ«Ð¦´Ò³Ñf œgη”´““ÛķÙ §µ™“ì”g¿Ñ¦§¿f Ò­«Ç× “. 3,665,800 ”. 36,658,000 –. 3,665,800,000 ™. 36,658,000,000 39. 36.658  108 Δ´Ç «Ð¦´Ò³fќgη”´““ÛÄ·™Ã §µ™“¬Ã ”g¿Ñ¦§f¿Ò­«Ç× “. 0.0000000036658 ”. 0.00000036658 –. 0.0000036658 ™. 0.000036658 40. (125  103  (0.002  107 ΔǴ«Ñ«µ­Ë ”¿™¼ÃŸ“µ¥¹ ©Æ ´ÄºÄ¼§µ §µ™“¬Ã ”¿g Ѧ§f¿Ò­«×Ç “. 2.5  107 ”. 2.5  108 –. 2.5  109 ™. 2.5  1010